It is often desirable to determine the attitude of a spacecraft for payload pointing purposes. Attitude refers to angular orientation of the spacecraft with respect to three orthogonal axes. Satellites typically employ attitude determination apparatus for pointing a payload such as a telescope or antenna to a desired location on the Earth. Conventional attitude sensing apparatus may include a satellite receiver such as a Global Positioning System (GPS), ground tracking apparatus for locating the satellite ephemerides, and star, sun or Earth sensors for transforming latitude, longitude and altitude information determined in spacecraft body coordinates into a stellar, or orbital frame of reference. Various methods have been used to process attitude sensor data to control spacecraft attitude.
Several methods of controlling spacecraft attitude using Extended Kalman Filter (EKF) based algorithms have been proposed to estimate the spacecraft attitude errors and gyroscope rate biases sing various attitude sensor data. For example, see E. J. Lefferts, et al., "Kalman Filtering for Spacecraft Attitude Determination," A.I.A.A. Journal on Guidance, Control and Dynamics, September.-October. 1982, pp. 417-429; A. Wu, "Attitude Determination for GEO Satellites," NASA Goddard 1997 Flight Mechanics Symposium, Greenbelt, Md., May 19-21, 1997.
The EKF is an established estimation method for attitude determination. In particular, the Kalman filter provides optimal noise attenuation performance for both process and measurement noises. EKF filtering is ideally suited for systems wherein disturbances are white noise processes. A steady state Kalman filter is a simple (fixed gain) estimator for state dynamics and measurement equations which are time-invariant. If either the state dynamics or measurement equations vary with time, however, the Kalman filter gains become time-varying. Existing EKF methods of attitude determination require the propagation of a 6.times.6 error covariance matrix between attitude observations in order to compute the time-varying Kalman filter gain matrix. Differential equations describing the error covariance propagation of a time-varying system necessarily includes matrix inversion operations. Such matrix propagation and updating requires intensive computations at each attitude processing cycle. These computations are beyond the capability of many current spacecraft control processors.
To reduce the computational complexity of such a system, a fixed gain filter approach can be used such as a TRIAD-based system. The TRIAD method of attitude determination is described in M.D. Shuster et al., "Three-Axis Attitude Determination From Vector Observations," Journal of Guidance and Control, vol. 4, no. 1, January-February 1981. A fixed gain approach to attitude determination reduces the computational complexity of the system, however, performance significantly deviates from the optimal solution provided by an EKF design because it ignores the time-varying measurement geometry in the filter design.